detailed balance principle

E267413

The detailed balance principle is a thermodynamic concept stating that, at equilibrium, every microscopic process is exactly balanced by its reverse process, ensuring no net change in the system’s macroscopic state.

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detailed balance principle canonical 1

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Predicate Object
instanceOf concept in statistical mechanics
thermodynamic principle
appliesTo microscopic processes
reversible Markov chains
systems in thermodynamic equilibrium
assumes existence of equilibrium state
reversibility of microscopic dynamics
category physical law
probabilistic constraint on dynamics
conditionType microscopic reversibility condition
contrastsWith global balance condition
coreIdea each microscopic process is balanced by its reverse at equilibrium
describes balance of microscopic transition probabilities at equilibrium
ensures no net macroscopic change in equilibrium state
no net probability current between microstates at equilibrium
time-reversal symmetry at equilibrium for many systems
field Markov processes
chemical kinetics
statistical mechanics
thermodynamics
goalInMCMC to make target distribution invariant under Markov chain transitions
historicalOrigin early 20th century development of kinetic theory and statistical mechanics
holdsWhen system is closed and isolated long enough to reach equilibrium
implies Boltzmann distribution for systems in canonical ensemble
stationary distribution of microstates
mathematicalForm π(i) P(i→j) = π(j) P(j→i) for all states i,j at equilibrium
mayFailWhen in presence of external fields driving steady currents
system is driven far from equilibrium
time-reversal symmetry is broken
relatedConcept Boltzmann distribution
Markov chain reversibility
Onsager reciprocal relations
equilibrium statistical mechanics
microscopic reversibility
relates forward transition rates and reverse transition rates
usedIn Gibbs sampling
Metropolis algorithm
surface form: Metropolis–Hastings algorithm

construction of Markov Chain Monte Carlo algorithms
derivation of Boltzmann equation
derivation of rate equations in chemical kinetics
kinetic theory of gases
radiative transfer theory
reaction network theory
semiconductor physics
usedToDerive Einstein relations in some transport processes
equilibrium relations between reaction rate constants

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Shockley–Queisser limit isBasedOn detailed balance principle